Available online at www.sciencedirect.com
Energy Procedia 00 (2013) 000–000
www.elsevier.com/locate/procedia
The Mediterranean Green Energy Forum 2013, MGEF-13
Characterization and Control of Supercapacitors Bank for
Stand-Alone Photovoltaic Energy
Benyahia N.a,*, Denoun H.a, Zaouia M.a, Tamalouzt S.b, Bouheraoua M.a,
Benamrouche N.a, Rekioua T.b, Haddad S.a
a
Laboratoire des technologies avancées en génie électrique (LATAGE),BP 17 RP 15000, Tizi-Ouzuo, Algérie
b
Laboratoire de technologie industrielle et d’information (LT2I),Targa-Ouzemour 06000, Bejaia, Algérie
Abstract
In this paper, a simple scheme of the supercapacitor based on (RC) circuit is modeled and characterized using
experimental methods. Then, computer simulations and experimental results showed very good agreement which
demonstrates the accuracy of the adopted model. An example of hybrid photovoltaic/supercapacitor stand-alone
system is considered in this paper. Dynamic model of photovoltaic system component is developed and validated
with experimental results. In addition, the maximum power point tracking (MPPT) control for photovoltaic and the
supercapacitor state of charge (SOC) control are also addressed in this work. Based on the dynamic component
models, a simulation model for the considered hybrid energy system has been developed using MATLAB/Simulink.
The simulation results show the primary role of the supercapacitor when the load changes rapidly.
© 20xx The Authors. Published by Elsevier Ltd.
Selection and peer-review under responsibility of KES International
Keywords: Supercapacitor, Photovoltaic, stand-alone;
1. Introduction
A growing interest in renewable energy resources has been observed for several years. The alternative
energy sources are non-polluting, free in their availability and continuous. These facts make the
alternative energy resources attractive in rural or energy deficient areas where the cost of connection to
the grid in remote locations cannot be justified [1]. Today, the most developed source of alternative
energy systems are: the solar energy and the wind energy.
* Corresponding author. Tel.: +213 26 21 46 28 ; fax:+213 26 21 61 52.
E-mail address: benyahia.ummto@yahoo.fr
Author name / Energy Procedia 00 (2013) 000–000
Nomenclature
ESR
equivalent series resistance
Lpv
boost converter filter inductance
C
bus filter capacitance
Lsc
bidirectional converter filter inductance
Vmpp
voltage at maximum power point
Impp
current at maximum power point
Voc
open circuit voltage
Isc
short circuit current
Ppv
photovoltaic power
Pbus
load power
Psc
supercapacitor power
Vscmax
supercapacitor maximum voltage
SOCr
supercapacitor state of charge reference
nbb
bidirectional dc-dc convertor efficiency
D
duty ratio
Dr
reference duty ratio
iscr
supercapacitor reference current
vLpv
boost converter filter inductance voltage
mes
measure value
ref
reference value
However, these renewable energy sources suffer from some deficiencies when used as stand-alone
energy sources. The natural intermittent properties of wind speed and sunlight causes power fluctuations
in wind turbine and photovoltaic panel systems. In addition it is difficult to store the power generated by
wind turbines and photovoltaic panels for future use [2,3]. For these reasons, energy storage is required to
manage the power flow and to maintain system instantaneous power balance. Generally, the energy
storage systems in stand-alone renewable sources can be batteries or supercapacitors.
In comparison to standard batteries, the energy density of super-capacitors is lower by an average
factor of 10. However, their energy density is compatible with a large range of power applications that
need high instantaneous power during short periods of time. Another advantage in the use of supercapacitors rather than batteries is their life time and their number of cycles, which is at least 500 times
more than that of standard batteries [4]. In addition super-capacitors are electrical energy storage devices
that offer significantly better energy densities than conventional capacitors and can be constructed in
Author name / Energy Procedia 00 (2013) 000–000
modular and/or stackable format [5–9]. The charge and discharge times of a super-capacitor varies from
fractions of a second to several minutes while providing maintenance free operation. Super-capacitors
provide the lowest cost per farad, extremely high cycling capability and are environmentally safe.
This paper is dedicated mainly to characterize the supercapacitors bank. Then, the simple model of
supercapacitor called RC model is considered. An experimental test of the supercapacitors bank is
performed and the results are discussed. An example of photovoltaic (PV)/supercapacitor (SC) hybrid
system is considered in this paper. Then, the modeling and control of this system is represented. Dynamic
models for the main system components, namely, PV energy conversion system and supercapacitors
bank, are developed and validated by experimental results. The maximum power point tracking (MPPT)
control for the PV system, and the state of charge control for the supercapacitor, are also addressed in this
work. Based on the dynamic component models, a simulation model for the proposed hybrid system has
been developed using MATLAB/Simulink. The overall power management strategy for coordinating the
power flows among the two energy sources is discussed. Simulation studies have been carried out to
verify the system performance under load and weather variation profiles. The results show that the overall
power management strategy is efficient and the power flows among the different energy sources and the
load demand is balanced successfully.
2. Supercapacitor modeling and characterization
Many models of the supercapacitors are proposed in the literature [10], the model developed by
Zubieta and Bonert [11] can be used. This model takes into account a non-linear equivalent capacitance
(Co and Cu), a leakage resistor (Rl), a series resistor (Rs), and relaxation phenomenon (R1, C1; R2, C2; …;
Rn, Cn ). This model is known by its accuracy. However its implementation in Matlab/simulink software
necessitates a very long time period which makes it impossible to apply. In this paper, the characterization
of the supercapacitor is based on a simplified RC model, its consists of a non linear capacitance C(vsc), an
equivalent series resistance (ESR) and a rated capacitance Ccd, as shown in Fig. 1. This simplified model
is suitable for applications where the energy stored in the capacitor is of a primary importance [10-11].
Fig. 1. Simplified RC circuit of the supercapacitor
The schematic diagram bench used to identify the parameters of the supercapacitor is showed in Fig. 2.
The diagram is composed of a bidirectional dc-dc converter with its smoothing inductance, Maxwell
BOOSTCAP units (BMOD Series), and a dSPACE 1103 card. The supercapacitor use non-water soluble
electrolyte technology. The energy storage bank is composed of a branch with 7 supercapacitors under
105 V with a resistive balancing. According to the manufacturer’s information, the branch of
supercapacitors composes an 8.3 F – 105 V supercapacitor based energy storage unit. The configuration
of the characterization bench system was implemented in the CRTT laboratory (Saint-Nazaire, France).
The current and voltage sensors are used to measure the super-capacitor voltages and currents.
Author name / Energy Procedia 00 (2013) 000–000
In this paper, the constant current tests method is used to determine the supercapacitor branch
parameters. Constant current tests represent a basic and a widely used characterization method that is
useful to determine the rated capacitance and the equivalent series resistance (ESR). Then, these
parameters can be determined for charge or discharge and for different current levels and ambient
temperatures [12].
Fig. 2. Characterization bench
26
(Vd , td)
Su p e rc a p a c ito r v o lta g e Vs cap [V ]
25
24
20.4
23
22
28.19
21
(Vc , tc)
20
24.2
23.86
19
18
43.17
17
0
10
20
30
40
(Vo , to)
50
48.17
60
Time [s]
Fig. 3. Experimental response voltage cycles to 2 A test charge constant current.
This method is based on a succession of cycles, each made of a constant current charge from (Vd) up to
(Vc) separated by a rest period (td-tc = 5 s) during which the open-circuit voltage (Vo) is measured.
Therefore, the use of Eqs. (1) and (2) allows for the calculation of the averaged rated capacitance (Ccd)
and the averaged equivalent series resistance using the parameters showing in Fig. 3. This figure
illustrates the evolution of the supercapacitor voltage measured at current switch-off after 2A constant
current charge with an ambient temperature of 25 ◦C. This method allows the determination of averaged
resistance (ESR) and averaged rated capacitance Ccd. Their values are given in Table.1.
Author name / Energy Procedia 00 (2013) 000–000
ESR 
C cd 
n
1
n  I sc
I sc
n
C V sc  
Vc
i
 Voi
(1)
i 0
n
tc i  td i
i  Vd i
 Vo
i 0
(2)
I sc
dV sc
dt
(3)
Fig. 4 shows the linear dependency of capacitance with voltage; the slope of the capacitance versus
voltage curve is about 0.95 F V-1. The effect of the non-linearity is taken into account in the model of the
supercapacitor. Fig. 5 illustrates the evolution of the simplified model voltage compared to the measured
voltage at 2 A constant current charge and discharge. The two sets of results give a good fit apart from the
noise observed on the experimental voltage.
13
C(Vsc)
12
Measured Ccd
Manufactured Ccd
Capacitor [F]
11
10
9
8
7
6
5
5
6
7
8
9
Voltage [V]
10
11
12
Fig. 4. Linear dependency capacitance with voltage and measured rated capacitance.
Table 1. Supercapacitor parameters
Parameters
Manufactured
Characterized
Ccd [F]
8.3
8.66
ESR []
0.15
0.17
-
0.95
-1
K [F.V ]
V o lta g e [V ]
Author name / Energy Procedia 00 (2013) 000–000
Measured
Simulation
9
8
7
C u rre n t [A ]
0
5
10
15
Time [s]
20
25
30
2
0
Measured
Simulation
-2
0
5
10
15
20
25
30
Time [s]
Fig. 5. Experimental and simulated responses of the supercapacitor branch.
3. Photovoltaic model
The most commonly used model for a PV cell is the one-diode equivalent circuit as shown in Fig. 6
[13, 14]. Since the shunt resistance Rsh is large, it normally can be neglected. The five parameters model
shown in Fig. 6(a) can therefore be simplified into that shown in Fig. 6(b).
Fig. 6. One-diode equivalent circuit model for PV cell.
(a) five parameters model; (b) simplified four parameters model.
This simplified equivalent circuit model is used in this study. The PV cell model is generally
represented by the following expressions
(4)
I pv  I ph  I d
 
 
(5)
I d  I 0 exp (V pv  Rs I ) / Vt  1


I ph  G / Gref I ph,ref   I Tc  Tc,ref

(6)
Author name / Energy Procedia 00 (2013) 000–000
Where Iph is the light current, Ipv is the load current and I0 is the saturation current. The Vpv is the output
voltage, Rs is the series resistance, the Vt is the thermal voltage, G is the irradiation, Tc is the cell
temperature and I is the temperature coefficient. The main PV parameters are shown in Table.2.
Table 2. PV panel parameters
Parameters
Characterized
Vmp (V)
17.1
Imp (A)
4.70
Voc (V)
21.9
Isc (A)
4.97
Pmax(W)
80.0
4. Hybrid system control
In this section, a hybrid stand-alone PV/supercapacitor power generation systems is investigated. The
system is controlled in a way that during a load transient the PV provides the steady-state load, and the
supercapacitor will supply the transient load. The supercapacitor SOC is controlled to remain within a
desired range. Meanwhile, the PV output power is controlled by MPPT device. The dynamic models for
PV and supercapacitor, discussed in sections 2 and 3, are used in this section for simulation study. Fig. 7
shows the schematic diagram for the proposed PV and supercapacitor power generation system.
In order to allow the PV panel and the supercapacitor work efficiently, both the PV panel and the
supercapacitor are connected to the DC bus through a converter, where a boost dc-dc converter is used for
PV system to implement the MPPT technique and a bidirectional dc-dc converter is used to control the
supercapacitor SOC.
The supercapacitor is allows operates at charge and discharge mode in different scenarios. Like the PV,
the rating voltage of the supercapacitor is generally lower than the dc bus voltage. Or it's expected to be
lower so that the volume and size of the supercapacitor can be made smaller and the costs are reduced. So
when the power is transferred from the high-voltage dc bus to the low-voltage supercapacitor, a buck
converter is demanded. When the power is delivered from the supercapacitor to the dc bus, the voltage is
step up, and a boost converter is needed.
4.1. Supercapacitor control
The supercapacitor operating voltage can be maintained within a band by appropriate sizing of the
supercapacitor and enforcing upper and lower bounds on the SOC. The rate of change in supercapacitor
state of charge is proportional to the charging current isc
d
1
SOC 
isc
dt
C sc Vsc max
(7)
The power demand of the load is satisfied by sharing the current load demand between the photovoltaic
panel and the supercapacitor energy storage system. In steady state, the current delivered by the
bidirectional dc-dc converter from the supercapacitor can be expressed as [15]
Author name / Energy Procedia 00 (2013) 000–000
isc _ b 
v sc
isc  ibus  i pv
v pv nbb
(8)
Thus, the reference of the supercapacitors SOCr can be estimated using the following equation
v pv nbb
d
SOC r 
ibus  i pv
dt
C sc Vsc maxVsc


(9)
Fig. 7. PV panel and supercapacitor hybrid controller system scheme.
4.2. Photovoltaic system control
In order to extract the maximum available power from a PV array, it is necessary to operate the PV
array at its maximum power point (MPP). The MPP tracker device is a high-frequency boost dc-dc
converter inserted between the PV array and the dc bus, and it takes the dc input from the PV array,
convert it to a different dc voltage and current to exactly match the PV array to the dc bus. The dynamic
model of the boost dc-dc converter is given by the following equations
v pv  L pv
di pv
dt
i pv 1  D   C
 1  D vbus
dvbus
 ibus
dt
(10)
(11)
Author name / Energy Procedia 00 (2013) 000–000
4.3. Simulation results
The PV panel works in a specific area to guarantee the optimum efficiency. If photovoltaic output
power matches the requirement of the load, the photovoltaic will be the only source to supply the loads. If
there is a difference between photovoltaic supply and the load demand, the supercapacitor will fill in the
gap.
Fig. 8 shows that when (ipv-ibus > 0), there is an excess in power. The available power is used for
supercapacitor charging. When (ipv-ibus < 0), the PV generated power is not sufficient to supply the load
demand, the supercapacitors bank in discharging mode and PV panel operate together for produce the
required power.
3
2
Current (A)
1
0
-1
ipv mes
-2
ipv ref
isc mes
-3
isc ref
-4
0
50
100
150
200
250
Time (s)
300
350
400
450
Fig. 8. PV panel and supercapacitor currents.
5. Conclusion
In this paper, a supercapacitor for stand-alone applications has been modelled and characterized.
Moreover, a simple methodology based on the constant current tests has been used. Experimental results
show that the developed model of the supercapacitor reproduces the dynamic characteristics. Adding, a
supercapacitor auxiliary power sources to PV panels can reduce the PV’s size and cost. With the further
comparison among other alternative sources, the supercapacitor is selected as the auxiliary source to assist
the PV panel because of its high power density, quick response and long life time.
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